Publications [#345593] of Mark Haskins

Papers Published

1. Haskins, M; Kapouleas, N, Closed twisted products and SO(p) × SO(q)-invariant special Lagrangian cones, Communications in Analysis and Geometry, vol. 20 no. 1 (January, 2012), pp. 95-162 [doi]
   (last updated on 2024/04/23)

   Abstract:
   We study a construction we call the twisted product; in this construction higher dimensional special Lagrangian (SL) and Hamiltonian stationary cones in Cp+q (equivalently special Legendrian or contact stationary submanifolds in S2(p+q)?1) are constructed by combining such objects in Cp and Cq using a suitable Legendrian curve in S3. We study the geometry of these "twisting" curves and in particular the closing conditions for them. In combination with Carberry-McIntosh's continuous families of special Legendrian 2-tori [3] and the authors' higher genus special Legendrians [13], this yields a constellation of new SL and Hamiltonian stationary cones in Cn that are topological products. In particular, for all n sufficiently large we exhibit infinitely many topological types of SL and Hamiltonian stationary cone in Cn, which can occur in continuous families of arbitrarily high dimension. A special case of the twisted product construction yields all SO(p) × SO(q)-invariant SL cones in Cp+q. These SL cones are higher-dimensional analogues of the SO(2)-invariant SL cones constructed previously by Haskins [8, 10] and used in our gluing constructions of higher genus SL cones in C3 [13]. SO(p) × SO(q)-invariant SL cones play a fundamental role as building blocks in gluing constructions of SL cones in high dimensions [14]. We study some basic geometric features of these cones including their closing and embeddedness properties.